Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T10:46:45.245Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimum Variance Unbiased Estimation of Software Reliability

Published online by Cambridge University Press:  27 July 2009

Tapan K. Nayak
Tapan K. Nayak
Affiliation:
Department of StatisticsGeorge Washington University Washington, D.C. 20052
Get access Rights & Permissions [Opens in a new window]

Abstract

As the formal methods of proving correctness of a computer program are still very inadequate, in practice when a new piece of software is developed and all obvious errors are removed, it is tested with different (random) inputs in order to detect the remaining errors and assess its quality. We suppose that whenever the program fails the error causing the failure can be detected and removed correctly. Thus, the quality of the software increases as testing goes on. In this paper, we consider two different models and present the minimum variance unbiased estimators of the expected failure rate of the revised software at any time of testing t, based on the data generated up to that point.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 3 , July 1989 , pp. 335 - 340
Copyright
Copyright © Cambridge University Press 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Clayton, M.K. & Frees, E.W. (1987). Nonparametric estimation of the probability of discovering a new species. Journal of the American Statistical Association 82: 305–311.CrossRefGoogle Scholar
Derman, C. & Koh, S.P. (1988). On the comparison of two software reliability estimators. Probability in the Engineering and Informational Sciences 2: 15–21.CrossRefGoogle Scholar
Jelinski, Z. & Moranda, P.M. (1972). Software reliability research. In Freiberger, W. (ed.), Statistical computer performance evaluation. New York: Academic Press, pp. 465–484.CrossRefGoogle Scholar
Langberg, N. & Singpurwalla, N.D. (1985). Unification of some software reliability models. SIAM Journal of Scientific Computing 6: 781–790.CrossRefGoogle Scholar
Nayak, T.K. (1986). Software reliability: statistical modeling and estimation. IEEE Transactions on Reliability R-35: 566–570.CrossRefGoogle Scholar
Nayak, T.K. (1988). Estimating population size by recapture sampling. Biometrika 75: 113–120.CrossRefGoogle Scholar
Nayak, T.K. (1989). A note on estimating the number of errors in a system by recapture sampling. Statistics and Probability Letters 7: 191–194.Google Scholar
Robbins, H. (1968). Estimating the total probability of the unobserved outcomes of an experiment. Annals of Mathematical Statistics 39: 256–257.CrossRefGoogle Scholar
Ross, S.M. (1985). Statistical estimation of software reliability. IEEE Transactions on Software Engineering SE-11(5): 479–483.CrossRefGoogle Scholar
Ross, S.M. (1985). Software reliability: the stopping rule problem. IEEE Transactions on Software Engineering SE-11 (12): 1472–1476.Google Scholar
Starr, N. (1979). Linear estimation of the probability of discovering a new species. Annals of Statistics 7: 644–652.CrossRefGoogle Scholar